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Contents Number 1 2 3 4 5 6 7 8 9 10 11 12 13
Whole numbers 1 Whole numbers 2 Decimals 1 Decimals 2 Fractions Percentages Ratio and proportion Addition and subtraction 1 Addition and subtraction 2 Addition and subtraction 3 Multiplication and division 1 Multiplication and division 2 Multiplication and division 3
2 18 26 34 42 58 66 74 82 98 106 114 130
Geometry 14 15 16 17
2D shape 3D shape Angles Position and movement
146 154 162 170
Measure 18 19 20 21 22
Length Mass Capacity Time Area and perimeter
186 194 202 210 218
Handling data 23 Handling data
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Unit
15 3D shape
Lesson 1: Visualising 3D shapes Geometry
• Visualise and describe the properties of 3D shapes, e.g. faces, edges and vertices Challenge
1 Count the shapes and complete the table. Shape
Number
cube cuboid tetrahedron (triangular-based pyramid) square-based pyramid triangular prism pentagonal prism
Challenge
2
1 Draw lines to match each pyramid to the shape of its base. square pentagon octagon triangle hexagon
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2 Complete the table. Remember a base is the ‘bottom’ face of a pyramid or cone and the ‘bottom’ and ‘top’ faces of a prism or a cylinder. Edges are considered to be straight, not curved, and faces are considered to be flat. 3D shape
Number of bases
Shape of bases
Number of faces
Number of vertices
Number of edges
sphere
Geometry
Student’s Book page 77
cylinder cone cube cuboid triangular prism tetrahedron square-based pyramid pentagonal prism hexagonal pyramid heptagonal prism (7-sided) octagonal pyramid Challenge
3 Answer these word problems. Show your working out. a
Latisha has 4 triangular prisms, 3 cubes and 5 tetrahedrons. Amelia has 3 square-based pyramids, 4 pentagonal prisms and 3 octahedrons. How many more faces do Amelia’s shapes have than Latisha’s shapes?
b
Ben has 3 pentagonal prisms, 4 cuboids and 2 tetrahedrons. Yoko has 5 square-based pyramids, 4 hexagonal prisms and 5 octahedrons. How many more faces do Yoko’s shapes have than Ben’s shapes?
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Unit
15 3D shape
Lesson 2: Constructing 3D shapes Geometry
• Recognise, describe and build simple 3D shapes
You will need • ruler • 3D shapes: cuboid, tetrahedron, triangular prism, hexagonal pyramid, hexagonal prism
Challenge
1 Draw the ‘skeleton’ of a cube in the box and answer the questions.
a How many straight edges did you draw? b How many joins did you make? c Mark and label one pair of parallel edges. d Mark and label one pair of perpendicular edges. Challenge
2
1 Name the shape and state the number of faces, vertices and edges. Sketch the base and side faces.
Shape
No. of No. of faces vertices
No. of Sketch of base edges
Sketch of side faces
Name:
Name:
Name:
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Student’s Book page 78
b
How many straight edges are there?
c
How many joins have you drawn?
d
How many faces does the shape have?
e
Mark and label the apex.
Geometry
2 A 7-sided polygon is called a heptagon. Draw the ‘skeleton’ of a pyramid with a heptagonal base in the box and answer the questions. a What is the name of this shape?
Challenge
3 Euler’s Formula states: For any solid shape made of plane surfaces, the
number of faces plus the number of vertices, minus the number of edges, always equals 2. This can be written: F + V − E = 2. Complete the table to show that the formula is correct.
Shape triangular-based pyramid (tetrahedron) triangular prism
Vertices
Edges
Faces
F+V−E=
cube
square-based pyramid
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Unit
15 3D shape
Lesson 3: Nets (1) Geometry
You will need • coloured pencils
• Use knowledge of the properties of cubes to identify and draw different nets of cubes Challenge
1 Visualise the folded net
in your mind. Will it form a closed cube? Circle Yes or No. Yes
No
Explain your answer.
Challenge
2
1 Tick all the nets that will build a closed cube and will not have any faces that overlap. B
A
C
D
H
F
I
E
J
G
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2 In the grid below, colour the squares to create as many nets for a closed cube as you can.
Geometry
Student’s Book page 79
Challenge
3 Which of the following nets will make a cuboid (rectangular prism)? Tick Yes or No and explain your answer. Net Yes A
No
Explanation
B C
A
B
C
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Unit
15 3D shape
Lesson 4: Nets (2) Geometry
• Use knowledge of prisms and pyramids to identify and draw nets of these shapes Challenge
1 Look at the diagrams and answer the questions.
Example The square-based pyramid is made up of
one square and four triangles. a
The triangular-based pyramid (tetrahedron) is made up of
. b
The triangular prism is made up of
. c
The pentagonal prism is made up of
.
Challenge
2 Decide whether each of the nets at the top of the next page will form a prism, a pyramid, or a shape that is NOT solid. Write the letter of each shape in the correct part of the table. Prism
Pyramid
Does not form a solid shape
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Student’s Book page 80
C
D
C
Geometry
A
E
F G H
Challenge
3 Which of the following nets will make a square-based pyramid? Tick Yes or No and explain your answer.
Net Yes No A
Explanation
B C A
B
C
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